A statistical analysis method for probability distributions in Erdös–Rényi random networks with preferential cutting–rewiring operation - Qian, Yu; Cao, Jiahui; Han, Jing; Zhang, Siyi; Chen, Wentao; Lei, Zhao; Cui, Xiaohua; Zheng, Zhigang (Frontiers in Network Physiology, 2024)
Recently, the study of the specific physiological processes from the perspective of network physiology becomes a hot issue, in which modelling the global information integration among the separated functionalized modules in structural and functional brain networks is a central problem. In this paper, the preferentially cutting-rewiring operation (PCRO) is introduced to approximatively describe the above physiological process, which consists of the cutting procedure and the rewiring procedure with specific preferential constraints. By applying the PCRO on the classical Erdös-Rényi random network (ERRN), three types of isolated nodes are generated, based on which the common leaves (CLs) are formed between the two hubs. This makes the initially homogeneous ERRN experience drastic changes and become heterogeneous. Importantly, a statistical analysis method is proposed to theoretically analyze the statistical properties of the ERRN with PCRO. Specifically, the probability distributions of these three types of isolated nodes are derived, based on which the probability distribution of CL can be obtained easily. Furthermore, the validity and the universality of our statistical analysis method have been both confirmed in numerical experiments. Our contributions may shed lights on a new perspective in the interdisciplinary field of complexity science and biological science and would be of great and general interests for network physiology.